Two Republican senators said Tuesday that they've personally urged the Egyptian government to release Muslim Brotherhood prisoners, after hosting meetings with top officials in Cairo as part of an Obama administration-sanctioned visit.

Sen. John McCain, R-Ariz., who is in Cairo along with Sen. Lindsey Graham, R-.S.C., made clear that the two U.S. lawmakers are representing the views of Congress and "do not speak for the White House."

Still, they are among the most prominent U.S. representatives in the country this week, as a wave of international mediators tries to nudge the country's military-backed government to resolve the standoff with supporters of ousted president Mohammed Morsi.

Egypt's interim presidency denounced "foreign pressure" in a sign of its growing impatience with international mediations.

But McCain and Graham said they urged Egypt's government to release Islamist prisoners supportive of Morsi before starting negotiations. He said those negotiations should include the Muslim Brotherhood.

"We have urged a national dialogue that is inclusive of all parties that will renounce the use of violence. We have strongly urged a set timetable for amending of the constitutions, elections for the parliament followed by elections to the presidency," McCain said.

McCain said the senators' "main message" is that democracy is the only path to lasting stability. He called on all sides to refrain from violence.

Graham said his "worst nightmare" is that Egypt fails. Addressing the concerns of Morsi's many detractors, Graham said that while he believes Morsi was brought to office in a free election, "millions of Egyptians were upset at the way this country was being governed."